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Science and Mathematics Education Commons™

Open Access. Powered by Scholars. Published by Universities.®

2015

Physical Sciences and Mathematics

Harish Chandra Rajpoot H.C. Rajpoot

Articles 1 - 3 of 3

Full-Text Articles in Science and Mathematics Education

Derivation Of The Volume Of Tetrahedron/Pyramid Bounded By A Given Plane & The Co-Ordinate Planes, Harish Chandra Rajpoot Rajpoot Hcr Nov 2015

Derivation Of The Volume Of Tetrahedron/Pyramid Bounded By A Given Plane & The Co-Ordinate Planes, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

The article here deals with the derivation of a general expression to calculate the volume of tetrahedron/pyramid bounded by a given plane & the co-rdinate planes (i.e. XY-plane, YZ-plane & ZX-plane) using intercept form of equation of a plane in 3-D space. All the derivations are based on simple geometry. These are very useful to directly calculate the volume of the bounded tetrahedron/pyramid.

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Mathematical Analysis Of Sphere Resting In The Vertex Of Right Pyramid & Polyhedron, Filleting Of The Faces & Packing Of The Spheres In The Vertex, Harish Chandra Rajpoot Rajpoot Hcr Jun 2015

Mathematical Analysis Of Sphere Resting In The Vertex Of Right Pyramid & Polyhedron, Filleting Of The Faces & Packing Of The Spheres In The Vertex, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

The generalized formula derived here by the author are applicable to locate any sphere, with a certain radius, resting in a vertex (corner) at which n no. of edges meet together at angle α between any two consecutive of them such as the vertex of platonic solids, any of two identical & diagonally opposite vertices of uniform polyhedrons with congruent right kite faces & the vertex of right pyramid with regular n-gonal base. These are also useful for filleting the faces meeting at the vertex of the polyhedron to best fit the sphere in that vertex. These are used to …

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Identical Circles Touching One Another On A Whole (Entire) Spherical Surface, Harish Chandra Rajpoot Rajpoot Hcr May 2015

Identical Circles Touching One Another On A Whole (Entire) Spherical Surface, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

All the articles discussed & analysed here are related to all five platonic solids. A certain no. of the identical circles are touching one another on a whole (entire) spherical surface having certain radius then all the important parameters such as flat radius & arc radius of each circle, total surface area & its percentage covered by all the circles on the sphere have been easily calculated by using simple geometry & table for the important parameters of all five platonic solids by the author Mr H.C. Rajpoot. These parameters are very useful for drawing the identical circles on a …

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